An alternative approach is to approximate the solution of differential equations by a neural network which is trained to satisfy a given set of differential equations, initial and boundary conditions.
This approach is known in the literature under the name of physics-informed neural networks (PINN) [1]}, [2]} and it can be seen as a machine learning alternative to the classical numerical solvers.
Despite the conceptual simplicity and elegancy of the method, training PINNs is notoriously difficult in practice [3]}, [4]}. It requires balancing of multiple terms in the loss function [3]}, [6]} and the commonly used neural network architectures and parameter initialization schemes may not work best for PINNs [7]}, [8]}.
